I've had the same problem. I've found that if I log in and then immediately click on "Messages" in the upper right corner, I can stay logged in for the rest of that session. I'm not sure why that works, or if it will work for others of you...

After posting this thread I accidentally discovered that I stayed logged in if I went to the forum right after initially logging in. It's inconvenient but it's good to have a work-around. Thanks for the replies!

I just sent a message to admin again about this again. It's so weird--the other Puzzle Baron websites I've visited allow you to stay logged in, no problem. I wonder how many solvers don't discover this trick of staying logged in and either give up on dropquotes or just play as guests (and thus aren't eligible for any of the monthly contests or record solving times).

It's the same problem we've had for over a year--when I log in, then click "Play," the site often logs me back out so I'm playing as "Guest." The trick I described above--log in, then click on "Messages," still works, but as I said, many solvers may not discover that trick.